Question

the octagon below is rotated around the line segment pq
which solid results from the rotation?

Explanation:

Analyze the 2D shape and axis of rotation

$$ \text{Shape: Regular octagon} $$

$$ \text{Axis of rotation: Line segment } PQ \text{ passing vertically through the center of the top and bottom horizontal edges} $$

Determine the cross-sectional behavior of the rotated parts

$$ \text{Top and bottom horizontal edges: Rotate to form flat circular bases} $$

$$ \text{Upper and lower slanted edges: Rotate to form conical frustums (slanted surfaces)} $$

$$ \text{Middle vertical edges: Rotate to form a central cylinder} $$

Identify the resulting 3D solid

$$ \text{Solid structure: A central cylinder with a conical frustum attached to both its top and bottom bases} $$

Answer:

• (A) A cylinder with a conical frustum on the top and a conical frustum on the bottom (Correct answer)